I() =< |U 2 | > +2 < |V 2 | > i < |U V V U | > 0,
(9)
The minimum value of I(), as a function of , is reached when I/ = I/ = 0.
This condition implies that
2(B)2 = i < [A, B] >,
=>
=
i < [A, B] >
.
2(B)2
Substituting this expression for into Eq. (9), we o
36
Homonuclear Diatomic Molecules
Other homonuclear diatomic molecules (e.g., Li2 , O2 , He2 , F2 , N2 , .) can be described ac+
cording to the LCAO approach introduced with the study of the H2 molecule. A general feature
of the LCAO method is that a comb
2
The Fundamental Postulates of Quantum Mechanics
Quantum Mechanics can be formulated in terms of a few postulates (i.e., theoretical principles
based on experimental observations). The goal of this section is to introduce such principles, together with s
26
Hydrogen Atom
Consider the hydrogen atom, or hydrogen-like ions (e.g., He+ , Li2+ , . etc.), with nuclear charge
+ze, and mass M , and the electron with charge e, and mass m. The potential energy of the
system is a central potential (e.g., the Coulombi
38.1
Restricted Closed Shell Hartree-Fock
The so-called closed-shell restricted Hartree-Fock method is essentially the Hartree-Fock approach
implemented for systems with an even number n of electrons, with each orbital j populated by 2
electrons with oppo
32
Periodic Table
Previous sections of these lectures have discussed the electronic structure of H, He and Li atoms.
The general approach implemented in those sections is summarized as follows. First, we neglect
the repulsive interaction between electrons
15.5
Schr dingers cat paradox:
o
A cat is placed in a steel box along with a Geiger counter, a vial of poison, a hammer, and a
radioactive substance. When the radioactive substance decays, the Geiger detects it and triggers
the hammer to release the poiso
22
Spin Angular Momentum
The goal of this section is to introduce the spin angular momentum S, as a generalized angular
momentum operator that satises the general commutation relations S S = i S . The main difference between the angular momenta S, and L,
Assume that the potential is described by perturbation W (x) = Sin( x ) to the particle in the
a
box.
13
Time Dependent Perturbation Theory
Given an arbitary state,R2(410)
(x, t) =
Cj j (x)e
i
Ej t
,
j
for the initially unperturbed system described by the
Theorem II
If > 0, state a| > is an eigenstate of N with eigenvalue equal to ( -1).
Proof:
In order to prove this theorem we need to show that,
N a| >= ( 1)| > .
a
(50)
We rst observe that,
[N , a] = .
a
Therefore,
[N , a] = a+ aa aa+ a,
, a] = [+